Tutorial on Introduction to
biostatistics

Diagnostic
tests used in clinical practices have certain operating
characteristics. It is important for clinicians to be aware of these
test characteristics as they interpret the results of these tests, and
also as they determine optimal testing strategies to get to an accurate
diagnosis or assign an appropriate prognosis. Sensitivity specificity,
positive predictive value and negative predictive values are key
parameters used in the further evaluation of the properties of
diagnostic tests. Diagnostic tests are compared to a “gold
standard” that is the best single test or combination of
tests that is relevant to the particular
diagnosis.

Sensitivity
is the chance that the diagnostic test will indicate the presence of
disease when the disease is actually present.

Specificity
is the chance that the diagnostic disease will indicate the absence of
disease when the disease is actually absent.

Positive
predictive value
is the chance that a positive test result actually means that the
disease is present.

Negative
predictive value
is the chance that a negative test result actually means that the
disease is absent

Note
that sensitivity depends only on the
distribution of positive and negative test results within the diseased
population and the specificity depends
only on the distribution of the results within the non-diseased
population. They do not depend on the ratio of diseased to
non-diseased and therefore are considered to be independent of disease
prevalence whereas positive
and negative predictive value is a function of disease prevalence and
pre-test probability.

Disease

+

_

Test

Present

True Positive (TP)

False Positive(FP)

Absent

False
Negative (FN)

True Negative (TN)

Sensitivity
= TP/(TP +FN)

Specificity
= TN/(TN + FP)

PPV
= TP/(TP + FP)

NPV
= TN/(TN + FN)

Efficiency
= (TP + TN)/(TP + FP + FN + TN)

The
mnemonics of “Spin” and “Snout”
(adapted from those originally suggested by Sackett and colleagues) are
extremely useful to remember the properties of specificity and
sensitivity. A highly specific (Sp) test, if positive (p) rules
“in” the disease – giving us Spin.
A highly sensitive (Sn) test, if negative (n) rules
“out” the disease – and there you have Snout.

Bayes
Theorem

Bayes’
theorem states the predictive value of a test will depend on the
prevalence of the disease.For diseases with high
prevalence, the positive predictive value will increase and vice versa.The negative predictive value
will have an opposite effect. If a researcher uses a diagnostic test in
a high prevalence setting, a positive test will be more likely to be
truly positive than in a low prevalence setting.

ROC
curves

ROC curves illustrate the
trade-off in sensitivity for specificity. The greater the area under
the ROC curve, the better the overall trade-off between sensitivity and
specificity. This is a more sophisticated way to determine the optimal
points for weighing sensitivity versus specificity since we know that
if one is increased, the other invariably tends to decrease.

Relative
Risk (RR):

Probability
of the disease if the risk factor is present divided by the probability
of the disease if the risk factor is absent.Example:a study to evaluate the
relationship between a food habit and diabetic might compare a group of
People with the specific food habit to a group not on the food habit
and follow them for the development of diabetic.If 10% of the people on the
food habit developed diabetic and 0.5% of the people not on the food
habit developed it, the relative risk would be 20.

Relative
risk of 1: no effect

Relative
risk >1: positive effect

Relative
risk <1: negative effect

Relative
risk should be presented with confidence intervals (CI), which to
reflect a statistically significant finding, should not contain data
points that include an RR of 1. Conversely, it can be seen that if the
RR CI does include
1, then the RR is not statistically significant.

In
the food habit /diabetic example If p value was 0.05 and the 95%
confidence interval for the relative risk of 20 was 0.7-25, then
statistical significance would not be achieved since the range of
values includes 1.

Odds
Ratio (OR):similar to relative risk, but
used for case-control studies.The odds of having the risk
factor if the disease is present divided by the odds of having the risk
factor if the disease is absent gives us the OR.

Likelihood
Ratio (LR)

Likelihood
ratios are very useful in that they are an indication of the degree to
which a test result will change the pre-test probability of disease.

It
can be calculated in two ways one is for a positive result and another
is for a negative result.

For
a given test, to get a positive likelihood ratio, the probability of a
positive test result if the disease is present divided by the
probability of a positive test result if the disease is absent.

+LR
= sensitivity/(1-specificity)

Probability
of a negative test result if the disease is present divided by the
probability of a negative test result if the disease is absent to get a
negative likelihood ratio.